Prime minister is fighting for his political future after support for his cabinet slumps

TOKYO—Japanese Prime Minister Shinzo Abe stumbled in an attempt to pull out of a career-threatening slump in popularity, reversing part of his response to allegations of cronyism and apologizing for what he called a mistake.

Mr. Abe is fighting for his political future after support for his cabinet fell below 30% in some opinion polls. A former vice education minister alleged the prime minister’s staff intervened last year to clear...